Vibration optimization of composite plates with multiple circular holes using two-dimensional sampling optimization method

Abstract

Perforated composite plates are widely used in engineering structures, and to prevent resonance, it is important to maximize the fundamental frequency. In this paper, the Ritz method is developed to calculate the vibration frequency of laminated composite plates with multiple circular holes, and the two-dimensional sampling optimization method (2DSO) is adopted to optimize the stacking sequence for achieving maximal fundamental frequency. Accounting for a variety of boundary conditions applied to the plate contour and circular holes, Legendre polynomials are adopted as admissible functions in the Ritz method in order to predict the vibration behavior of perforated plates. Then, 2DSO uses the lamination parameter (LP) to represent the distances between different stacking sequences. By generating uniformly distributed points in the LP design space and determining their corresponding stacking sequences, several good candidate stacking sequences are identified. Subsequently, local sampling optimization is employed to find better stacking sequences around the candidate stacking sequences. Lastly, the layerwise optimization approach (LOA) is employed to refine the sampling optimum. Perforated composite plates with one, two, and four circular holes, under different boundary conditions, are optimized. Results show the accuracy of the Ritz method, and the stability and efficiency of the 2DSO algorithm.